Math 2250: Differential Calculus

Welcome to the webpage for the applied math section of MATH 2250. This is a challenging course, which may not be suitable for all students. The course is aimed at students who are in the engineering program, the math education program, or considering a physical science major. The course provides serious professional training which prepares students for careers in these areas. Other students are always very welcome, but should understand that the course may not be targeted to them.

Here is the first class assignment: a diagnostic exam covering background material that you are expected to know in order to take this class. You will need to take the exam (and turn in your self-graded exam, along with a plan of action) during the first week of class.

Class Structure

This class is a fairly conventional lecture-based calculus class covering limits, differentiation, applications of differentiation to linear and quadratic approximation, max and min problems, and related rates, and an introduction to integration. The most important new feature of the course is a set of three in-depth lab activities based on the semester-long problem of programming a robot to throw a small object about a meter into a coffee cup. We’ll discover along the way that we need all the tools of first-semester calculus to build and program the robot, but our motivation will always be practical (with a few wonderful theories thrown in along the way for our education!). You’ll want to read the slides on How to write Mathematics like a Pro before writing your lab:

  1. Lab 1: Intercept a thrown tennis ball.
  2. Lab 2: Throw a ball with a robot.
  3. Lab 3: Hit a target with the robot.

At the end of the course, we have a practical exam with the robot in which you test your ability to get the robot to throw the projectile into a coffee cup. This handout helps you get organized for the practical.

The other main new features of the course are the early introduction of a weak form of Taylor’s theorem to unify the treatment of applications of differentiation as in Rob Ghrist’s Coursera Calculus Course and the required use of the spaced repetition software called Anki to aid in memorizing course material.

The objective of the lab projects is to provide the students a chance to integrate their calculus knowledge by working through a real-world application. The model for the lab is to prepare you for a career in a technical field by practicing writing a technical report for a client. Since we’re developing your writing and exposition skills as well as your mathematics, a substantial portion of the grading on these labs will be based on your explanation of the lab work.

If you’re curious about why we’re doing this, I encourage you to read this blog post about it and look at the first day slides.


The labs are regarded as course exams. In addition, there will be two in-class exams and an in-class final, giving a total of 5 exams in the course plus the final. Since the labs are exams, lab material will not be covered again on the in-class exams. Grades will be assigned according to the weights:

For a good discussion of how to interpret these grades, see Colm Mulcahy’s article on the Huffington Post: What do I have to do to get an A in this class?.

Additional Electronic Resources

  1. The 2250 Syllabus.
  2. We will use Mathematica for class demonstrations. You can always use the weaker free version of Mathematica available online as Wolfram|Alpha, but as a UGA math student, you can get the full version of Mathematica for free. Please ask me for details.
  3. The course will use the WebWork online homework system. The course homework is found here. You may encounter a browser error when you first visit the site, since our security certificate is not standard. It is ok to create an exception in Firefox or “continue to site” in Safari or Explorer, or “Proceed Anyway” in Chrome. This link gives detailed directions for creating exceptions. If you have trouble doing this with Internet Explorer, the best plan is really to switch to another browser, at least for homework. Chrome seems to do well with WebWork. Remember that your username is derived from your official UGA email address (so if your email is then your username is godawgs, not and your password is your nine digit 810 number without spaces, so if the 810 number on your id is 810 123 456 0, your password is 810123456.
  4. We are going to use Anki to help us memorize some required material in the course. Anki is a spaced repetition flashcard program based on psychology research which can significantly improve your ability to memorize things. Wired has a good article about the history of Anki. You need to download and install the software (it runs on Windows, Mac, Linux, Android, iPhone/iPod/iPad, and as a web-based application).
    1. Math 2250 Background Material Anki Deck (emergency backup pdf)
    2. Chapter 2 (Limits) Anki Deck
    3. Chapter 3 (Differentiation) Anki Deck
    4. Chapter 4 (Applications of Differentiation) Anki Deck
    5. Chapter 5 (Integration) Anki Deck
  5. You will also probably want to experiment with Wolfram|Alpha, which is one of the truly great web resources for calculus.
  6. The book for the class is University Calculus, by Hass/Weir/Thomas. We have reading assignments from the book, so you do need it.
  7. You can look at my notes for the first few lectures, although they are pretty minimal.
  8. The last class ended with a unit called Probability, Calculus, and Chicken exploring a probability application from operations research. I don’t think we’ll get to this during this semester (at the time I wrote it, I was fascinated by probability questions in calculus), but I’m leaving it up in case you’re interested.

Practice Exams and Exam Policies

Previous exams from this class are posted below for you to use for practice. I don’t provide answer keys to the exams on the web because when I did, nobody actually used them as practice exams (they just skip to the answer key as soon as they get stuck).

For exams, we’ll use the TI-30XS Multiview. (About $14 on Amazon.) I recommend that you bring it to class and practice with it. Even though we’ll have extra time during the exams, it’s always helpful to be comfortable with the technology that you’ll have on hand.

This class is now on the Math Department common final. The common final is intended to be a basic exam covering computational and conceptual questions which every calculus student should know after one semester of calculus. It is not intended to explore the outer boundaries of the syllabus, but to test the fundamentals.

How to succeed in this class

Material on this page is a work-for-hire produced for the University of Georgia.